局部Petrov-Galerkin方法在非线性边值问题中的应用  

A Meshless Local Petrov-Galerkin Method for the Solution of Nonlinear Boundary Value Problems

作　　者：胡德安[1] 龙述尧[2] 韩旭[1] 

机构地区：[1]湖南大学机械与汽车工程学院汽车车身先进设计制造国家重点实验室,湖南长沙410082 [2]湖南大学力学与航空航天学院,湖南长沙410082

出　　处：《湖南大学学报（自然科学版）》2007年第2期33-36,共4页Journal of Hunan University:Natural Sciences

基　　金：国家自然科学基金资助项目(10372030)

摘　　要：把一种真正的无网格局部Petrov-Galerkin方法用于求解非线性边值问题.为了克服一般局部Petrov-Galerkin方法计算工作量较大的问题,选择一个分段函数作为加权残值法的加权函数,简化了非线性问题中刚度矩阵的域积分.基于局部Petrov-Galerkin积分方程逐点建立的思想,推导了一种直接插值法用于施加本质边界条件.通过算例表明,这种局部Petrov-Galerkin方法是一种具有收敛快、精度高的方法.A truly meshless local Petrov-Galerkin （MLPG） method was presented to solve nonlinear boundary value problems. A simple Heaviside test function was chosen to overcome the computationally expensive problems. The computational effort was significantly reduced by simplifying the domain integral for the stiffness matrix in the MLPG method. Due to the MLPG method which establishes equations node by node, a direct interpolation method was proposed to impose essential boundary conditions. Numerical results show that the proposed method possesses high rates of convergence for the Sobolev norms with reasonably accurate results.

关 键 词：数值方法 局部Petrov—Galerkin方法 非线性边值问题 分段函数 

分 类 号：O302[理学—力学]